UNIONS-3500 Weak Lensing: III. 2D Cosmological Constraints in Configuration Space

arXiv:2605.13547 · astro-ph.CO · Submitted 2026-05-13 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: I'm Vera, and with me are Jocelyn and Subrahmanyan, guest researcher.

Jocelyn: Today's paper: "UNIONS-3500 Weak Lensing".

Vera: We present the first cosmological constraints from the cosmic shear analysis of the UNIONS-3500 weak lensing galaxy catalogue in configuration space.

Jocelyn: First, who's behind it and why it matters.

Title and authors: Vera: So, looking at the summary of "UNIONS-three thousand five hundred Weak Lensing: III. 2D Cosmological Constraints in Configuration Space," they are essentially describing a method using a single tomographic bin with the two-point correlation function statistic to analyze cosmic shear from their large catalogue.

Jocelyn: That's right, and they are setting up the framework for how they calculate that 2PCF, which is defined by the expectation value of the product of tangential and cross components of galaxy shear, xi plus or minus(theta) = xi t xi t(theta) plus or minus xi times xi times(theta) (one).

Subrahmanyan: They emphasize that this two-point correlation function captures similar information on the sky as other statistics, but they note it has different sensitivities to scales and masking effects, which is an important distinction for theoretical interpretation.

Vera: And they also detail how they model the cosmic shear observable as e obs = psi s + psi mu (five), where psi s is the true signal and psi mu is the magnification bias, which are both key ingredients in their analysis.

Jocelyn: It’s clear they aren't just looking at the raw signal; they are factoring in how galaxies distort and how magnification affects what we see, which adds a layer of complexity to the measurement process described in "UNIONS-three thousand five hundred Weak Lensing: III. 2D Cosmological Constraints in Configuration Space."

Subrahmanyan: The authors stress that their results are robust when they vary their analysis choices, specifically mentioning scale cuts, prior ranges, and nonlinear modeling, which helps show the stability of the inferred cosmological parameters.

Vera: That robustness is what makes these constraints reliable; it means the final S8 value they get isn't just an artifact of one specific way they chose to cut out data or model a certain aspect of galaxy clustering in configuration space.

Jocelyn: It sounds like the authors are really focused on showing that their pipeline, which includes everything from redshift estimation using a self-organizing map to shape measurement corrections, holds up under scrutiny.

The paper's summary: Vera: Now let’s talk about the specific improvements they suggest in this work and what they do to make the analysis more solid, because that is where the real progress is happening.

Jocelyn: They focus heavily on systematically assessing measurement effects by using techniques like configuration-space E/B-mode decomposition and referencing the Complete Orthogonal Sets of E/B-mode Integrals or COSEBIs (Schneider et al. two thousand ten; Asgari et al. two thousand twelve).

Subrahmanyan: The way they model PSF systematics using the equation epsilon sys = alpha PSF e p + beta PSF delta e p + eta PSF delta T p (eight) and then sampling those parameters at the inference step shows a sophisticated way to deal with those tricky instrumental biases.

Vera: That sounds like they are going beyond just a simple correction; they are letting the inference process itself help determine how much of that systematic error is present, which is quite advanced work for this kind of analysis.

Jocelyn: And their finding that there’s a non-negligible leakage bias at large scales for both data vectors really highlights why these systematic assessment step is so important in "UNIONS-three thousand five hundred Weak Lensing: III. 2D Cosmological Constraints in Configuration Space."

Subrahmanyan: They determined scale cuts based on the requirement that PSF systematics contribute less than ten percent of the total signal, leading to an upper scale cut of eighty-three arcmin for both xi plus or minus, which is a practical and necessary step for cleaner results.

Vera: So, they’re not just reporting a result; they are showing how to build a methodology that systematically addresses the known weaknesses of observational data sets before we even get to the cosmological parameters.

The paper's improvements: Jocelyn: So, as we wrap up this discussion on "UNIONS-three thousand five hundred Weak Lensing: III. 2D Cosmological Constraints in Configuration Space," the paper concludes by summarizing what they found regarding their constraints and why their results are considered competitive with other analyses.

Vera: They conclude that the resulting constraint on S8, which is S eight sigma eight sqrt m /zero point three = zero point eight three one pluszero point zero six seven-zero point zero seven eight, is consistent with constraints from Planck CMB measurements and other precedent cosmic shear results within one sigma.

Subrahmanyan: It’s a strong result because it bridges the gap between high-redshift CMB data and these lower-redshift weak lensing observations, which is exactly what we need to understand the structure of the universe across different epochs.

Jocelyn: That consistency is a solid foundation for our understanding, suggesting that whatever small tension exists might be better understood as a residual systematic effect rather than entirely new physics.

Vera: The paper demonstrates how rigorous pipeline development and systematic error mitigation can lead to competitive cosmological results from complex observational data like the UNIONS-three thousand five hundred survey.

Subrahmanyan: I think the implications for future surveys, like Euclid and LSST, are that they need to incorporate this level of systematic assessment right from the start if they want to get cleaner constraints on parameters like m.

Jocelyn: So we’ve seen how careful modeling of source distributions and calibration can significantly refine the final cosmological picture presented in "UNIONS-three thousand five hundred Weak Lensing: III. 2D Cosmological Constraints in Configuration Space."

Vera: It’s a lot of data, but when you process it with this level of care, you get constraints that are useful for testing our standard cosmological model.

Subrahmanyan: Indeed, the work solidifies the need for detailed modeling in configuration space analyses to move toward more precise cosmological parameter estimation.

Conclusion: Vera: So, we've been talking about "UNIONS-three thousand five hundred Weak Lensing: III. 2D Cosmological Constraints in Configuration Space," and now it’s time to wrap up how these constraints fit into the bigger picture for us.

Jocelyn: I agree, Vera, it was fascinating seeing how they handle those complex systematic effects like PSF leakage and redshift estimation in such a large catalogue.

Subrahmanyan: From a theoretical standpoint, what really stands out is the robust nature of their pipeline; showing that the results hold up even when you vary the analysis choices like scale cuts, that tells us we’re getting reliable physics from this data.

Vera: Exactly, Subrahmanyan, and those constraints on S eight being consistent with Planck measurements really gives us confidence in our current cosmological models.

Jocelyn: I'm also struck by the cross-correlation likelihood they develop to fuse different data sets, which is crucial for getting those tight constraints on m.

Subrahmanyan: That fusion capability is what makes these single-bin analyses so powerful when you combine them with other probes like CMB and BAO, showing how well the different cosmological pieces mesh together.

Vera: It’s clear that the maturity of this UNIONS data set is paying off by delivering these kinds of competitive cosmological results from configuration space analysis.

Jocelyn: And for those of us working on pulsar surveys, seeing how this weak lensing data complements our probes gives us a much richer view of the structure in the universe.

Subrahmanyan: Indeed, the implication here is that we can now place tighter bounds on cosmological parameters like S eight which directly impacts our understanding of dark energy and structure formation history.

Vera: It’s a great demonstration of how observational astronomy, when paired with careful methodology, can provide powerful constraints on fundamental physics.

Jocelyn: We definitely need to keep an eye on these results as future surveys come online because the systematic error mitigation techniques they used are exactly what we'll need for the next generation of data.

Subrahmanyan: That's a fair point; the focus now shifts to applying these lessons to even larger surveys and refining our theoretical predictions based on these tighter bounds.

Vera: So, that concludes our deep dive into "UNIONS-three thousand five hundred Weak Lensing: III. 2D Cosmological Constraints in Configuration Space," and we’re ready for whatever new paper comes next.

Institute for Astronomy, University of Edinburgh · Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh · Université Paris Cité, Université Paris-Saclay, CEA, CNRS · Department of Astronomy, Steward Observatory, University of Arizona · Ruhr University Bochum, Faculty of Physics and Astronomy (AIRUB) · NRC Herzberg Astronomy and Astrophysics · Department of Computer Science, University of Waterloo · Waterloo Centre for Astrophysics (University of Waterloo) · Perimeter Institute for Theoretical Physics (University of Waterloo) · Institute for Astronomy, University of Hawaii

astro-ph.CO

Submitted: 2026-05-13

Updated: 2026-05-13

Journal ref: Mon Not R Astron Soc (2026)

DOI: 10.1093/mnras/stag1774

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 83/100

The gist: We present the first cosmological constraints from the cosmic shear analysis of the UNIONS-3500 weak lensing galaxy catalogue in configuration space.

Key concepts

Cosmic Shear Analysis
This method analyzes how light from distant galaxies is distorted by intervening large-scale structure. It is used to measure cosmic shear, which provides information about the distribution of matter in the universe.
Two-point Correlation Function (2PCF)
The 2PCF is a statistic used to analyze cosmic shear. The authors define it using the expectation value of the product of tangential and cross components of galaxy shear, which helps capture similar sky information but has different sensitivities to scales and masking effects.
Systematic Error Mitigation
This involves systematically assessing measurement effects like PSF systematics using techniques such as configuration-space E/B-mode decomposition. The authors determined scale cuts based on keeping PSF systematics below ten percent of the total signal to ensure cleaner results.
S8 Constraint
The final result is a constraint on the parameter S8, which is related to the amplitude of matter fluctuations. The resulting value is consistent with constraints from Planck CMB measurements and other cosmic shear results within one sigma.

Terminology

Summary

We present the first cosmological constraints from the cosmic shear analysis of the UNIONS-3500 weak lensing galaxy catalogue in configuration space. The Ultraviolet Near Infrared Optical Northern Survey (UNIONS) is described as the largest and deepest photometric survey of the northern hemisphere to date, with the UNIONS-3500 catalogue using high-quality r-band imaging across 3500 deg2 of the sky. We perform a 2D cosmic shear analysis with a single tomographic bin, using the two-point correlation function (2PCF) statistic. Assuming a flat ΛCDM model, we obtain constraints on the clustering amplitude of S8 ≡ σ8√Ωm/0.3 = 0.831+0.067−0.078, which is stated to be consistent with constraints from Planck CMB measurements and precedent cosmic shear results within 1σ.

The paper outlines the construction of its cosmological inference pipeline, including the estimation of the source redshift distribution, shear calibration, and covariance matrix, and describes methodologies for the mitigation of systematic effects arising from PSF systematics and B-modes. The authors demonstrate that their results are robust to variations in analysis choices, including scale cuts, prior ranges, and nonlinear modelling. This paper is part of a coordinated release demonstrating the maturity of UNIONS to deliver competitive cosmological results.

The UNIONS data set combines multi-band photometric images from multiple telescopes: "The Canada-France Imaging Survey (CFIS) provides u- and r-band images from CFHT. The shape measurement of galaxies relies on high-quality images taken in the r band, which benefit from exquisite seeing of ∼0.7 arcsec, making it ideal for weak lensing science. The catalogue comprises over 61 million galaxies totalling an area of 3500 deg2, corresponding to 2894 deg2 of effective area after masking. Shapes were measured using ShapePipe (Farrens et al. 2022; Guinot et al. 2022), and calibration was performed using Metacalibration (Huff & Mandelbaum 2017; Sheldon & Huff 2017). The catalogue contains the spin-2 ellipticities for each galaxy, e1 and e2, corrected for the per-component additive biases c1 and c2. A size cut of rh,gal/rh,PSF > 0.7" was applied to create the fiducial catalogue.

The modeling details include:

In principle, these two statistics capture similar information on the sky, albeit with different sensitivities to scales and masking effects.

The cosmic shear 2PCF is defined as the expectation value of the product of the tangential and cross components of the galaxy shear signal, ξ±(θ) = ⟨ξt ξt⟩ (θ) ± ⟨ξ×ξ×⟩ (θ), (1) and its Fourier space counterpart is given by Equation (2). The cosmic shear power spectrum Cl is given by Equation (3). The cosmic shear observable is defined as e obs = ψ s + ψ μ (5).

Systematic effects are assessed through:

"We assess the robustness of our data vectors to systematic measurement effects, focusing on PSF modelling, configuration-space E/B-mode decomposition, and the Complete Orthogonal Sets of E/B-mode Integrals (COSEBIs; Schneider et al. 2010; Asgari et al. 2012)."

PSF systematic effects are modeled by e sys = αPSF e p + βPSF δe p + ηPSF δT p (8). The total observed 2PCF signal is expressed as ξ obs ±(θ; α, β, η) = ξ ψψ ±(θ) + ξ sys ±(θ; α, β, η) (12).

The authors found that a non-negligible leakage bias at large scales was detected for both the ξ± data vectors, and they modelled PSF systematics by additionally sampling the α and β parameters at the inference step. They determined scale cuts based on requirements that PSF systematics contribute less than 10% of the total signal, yielding an upper scale cut of 83 arcmin for both ξ±.

The redshift distribution is estimated using a method involving:

**"We train a self-organising map (SOM; Kohonen 1982), which arranges galaxies based on their positions in the multi-dimensional magnitude space... We then populate the SOM with the UNIONS sources by assigning each galaxy to its best-matching SOM cell based on its ugriz photometry.

Improvements for AI systems

As a fastidious researcher, I have analyzed this paper, UNIONS-3500 Weak Lensing: III, which details cosmological constraints from weak gravitational lensing using a large photometric survey.

The improvements suggested below focus on leveraging the methodology described in the paper—specifically the robust pipeline development and systematic error mitigation—to enhance AI systems in areas like cosmology, image processing, and machine learning model validation.

Here are the specific improvements and capabilities for an improved AI system:

)AI System Improvement: Cosmological Parameter Inference Engine (CPIE)

This improved system will integrate the Bayesian inference pipeline described in Section 4 with a sophisticated understanding of systematic degeneracies derived from the paper's extensive sensitivity analysis.

  1. Systematic Degeneracy Mapping and Prior Selection:

Improvement: The CPIE will move beyond simple flat/Gaussian priors for nuisance parameters like Intrinsic Alignment amplitude (AIA) and PSF leakage coefficients (α, β). Based on Section 5.2, the system will use a learned degeneracy map derived from the posterior distributions shown in Figure B1 and Figure B3.

Improvement: The system will dynamically select priors (e.g., Gaussian vs. Flat) for AIA and Δz based on the current data quality metric (e.g., effective degrees of freedom, chi2), mimicking the robust decision-making shown in Table B1 and Figure 13.

Capability: The CPIE can perform meta-inference, where it automatically adjusts its prior strategy in real-time to maximize the expected reduction in uncertainty for a target parameter (e.g., maximizing the constraint on Ωm while minimizing its impact on S8), effectively automating the nuanced trade-offs discussed in Section 5.2.

  1. Automated PSF and Redshift Calibration Correction:

Improvement: Integrate a modular component that directly executes the PSF systematics inference step described in Section 4.3, which fits parameters (α, β) using the derived ρ(θ) and τ(θ) statistics (Eqs. 9 & 10).

Improvement: The system will incorporate a mechanism to apply catalogue-level object-wise leakage correction (as tested in Figure 6), allowing it to toggle between object-wise corrected and uncorrected inputs based on the user's need or a learned correction confidence score.

Capability: This allows the AI system to produce self-calibrated cosmological constraints, reducing reliance on conservative, pre-determined systematic priors, thus achieving a higher effective degrees of freedom (e.g., moving from 14.5 to 75.33 in Table B1) and potentially breaking degeneracies between cosmological parameters and systematics.

  1. Nonlinear Modeling Adaptive Scaling:

Improvement: Implement a nonlinear model selector that compares the performance (PTE, goodness-of-fit) of different power spectrum modeling choices (HMCode2020 with feedback vs. without; Halofit).

Improvement: The system will dynamically adjust the scale cuts (e.g., 12 arcmin vs. 5 arcmin) based on the resulting impact on the S8 constraint, as explored in Section 4.6, rather than relying solely on a fixed fiducial choice.

Capability: The AI can automatically optimize its analysis by searching for the optimal combination of scale cuts and nonlinear model prescriptions to achieve the highest statistical significance (lowest PTE) for cosmological parameters, leading to more robust and less biased results (e.g., achieving the best-fit S8 value of 0.770+0.029−0.059 when IA is ignored).

)AI System Improvement: Weak Lensing Image Processing Module (WL-IPM)

This module will be trained on the image simulation and calibration data described in Paper V to improve the accuracy of shape measurement pipelines.

  1. **Adaptive PSF Modeling and Leakage Correction:**Improvement: Train a deep neural network (DNN) to learn the complex, non-linear relationship between observed ellipticity, PSF model parameters (size/ellipticity), and residual leakage terms (Eq. 8).

Improvement: The system will automatically apply the empirically derived correction factors or directly estimate the multiplicative bias parameter 'm' by analyzing input catalogue characteristics.

Capability: The WL-IPM can perform real-time shape deconvolution, producing a set of intrinsic ellipticities that are corrected for PSF contamination, leading to more accurate measurements than standard pipeline outputs, which is crucial for mitigating the multiplicative bias (m = -0.057 ± 0.014).

  1. **Automated Source Redshift Calibration:**Improvement: Integrate a learned version of the SOM redshift calibration technique (Section 3.3) into the image processing pipeline, allowing it to assign sources to photometric bins based on learned color-magnitude manifolds rather than relying solely on fixed cross-matches with external surveys like CFHTLenS.

Improvement: The system will incorporate the prior volume weighting scheme (Eq. 13) by training a model that learns the selection function differences between wide-field and spectroscopic samples to generate accurate weighting factors for simulated data.

Capability: This allows the system to produce highly accurate redshift distributions, minimizing the systematic shift Δz (-0.003), which is identified as a major source of parameter uncertainty in cosmological inference.

)AI System Improvement: Multi-Survey Data Fusion Framework (MSDF)

This framework will be designed to efficiently handle the combination of multi-source data sets described in Section 5.3.

  1. **Cross-Covariance Likelihood Integration:**Improvement: Develop a generalized likelihood function that explicitly accounts for the cross-correlations between different probes, specifically incorporating the lack of a prescribed covariance term between cosmic shear and CMB/BAO data (Section 3.6).

Capability: The MSDF can perform joint inference on UNIONS-3500, Planck CMB, and DESI BAO data simultaneously, yielding the combined constraints shown in Figure 16, significantly tightening the constraints on both S8 and Ωm.

  1. **Likelihood Adaptation for Likelihood Differences:**Improvement: The system will be designed to handle likelihood differences (e.g., between Planck's plik lite likelihood and the adopted Gaussian likelihood) by learning the necessary transformation or correction factors, as implicitly done in Section 3.6.1.

Capability: This allows the AI to seamlessly fuse data from different cosmological probes, even when their underlying statistical frameworks differ, leading to a more accurate final result than simple linear combination of marginalized posteriors.

Abstract

We present the first cosmological constraints from the cosmic shear analysis of the UNIONS-3500 weak lensing galaxy catalogue in configuration space. The Ultraviolet Near Infrared Optical Northern Survey (UNIONS) is the largest and deepest photometric survey of the northern hemisphere to date, with the UNIONS-3500 catalogue using high-quality r-band imaging across 3500 deg2 of the sky. We perform a 2D cosmic shear analysis with a single tomographic bin, using the two-point correlation function (2PCF) statistic. Assuming a flat LCDM model, we obtain constraints on the clustering amplitude of S 8 = 0.831+0.067-0.078, which is consistent with constraints from Planck CMB measurements and precedent cosmic shear results within 1sigma. We outline the construction of our cosmological inference pipeline, including the estimation of the source redshift distribution, shear calibration, and covariance matrix, and describe methodologies for the mitigation of systematic effects arising from PSF systematics and B-modes. We demonstrate that our results are robust to variations in analysis choices, including scale cuts, prior ranges, and nonlinear modelling. This paper is part of a coordinated release which collectively demonstrates the maturity and readiness of UNIONS to deliver competitive cosmological results, positioning it as a key stepping stone towards the forthcoming era of Stage IV weak lensing experiments.

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